Ideally, yes, they should be in the controller. I'm a bit more concerned that the cooler isn't showing up in Link. That one should, at least as long as the USB is connected. Look for the Corsair USBXP driver in Device Manager ... it may need a little kick ... disable and then enable it.
I would recommend going to iCue if you are using LInk but you'll lose your fan curves.
If moving from Link to iCue, look here for a tool to transfer the fan curves: